Kinetics methods for clinical epidemiology problems.

Calculating the probability of each possible outcome for a patient at any time in the future is currently possible only in the simplest cases: short-term prediction in acute diseases of otherwise healthy persons. This problem is to some extent analogous to predicting the concentrations of species in a reactor when knowing initial concentrations and after examining reaction rates at the individual molecule level. The existing theoretical framework behind predicting contagion and the immediate outcome of acute diseases in previously healthy individuals is largely analogous to deterministic kinetics of chemical systems consisting of one or a few reactions. We show that current statistical models commonly used in chronic disease epidemiology correspond to simple stochastic treatment of single reaction systems. The general problem corresponds to stochastic kinetics of complex reaction systems. We attempt to formulate epidemiologic problems related to chronic diseases in chemical kinetics terms. We review methods that may be adapted for use in epidemiology. We show that some reactions cannot fit into the mass-action law paradigm and solutions to these systems would frequently exhibit an antiportfolio effect. We provide a complete example application of stochastic kinetics modeling for a deductive meta-analysis of two papers on atrial fibrillation incidence, prevalence, and mortality.

Stability and sustained oscillations in a ventricular cardiomyocyte model.

The Luo-Rudy I model, describing the electrophysiology of a ventricular cardiomyocyte, is associated with an 8-dimensional discontinuous dynamical system with logarithmic and exponential non-linearities depending on 15 parameters. The associated stationary problem was reduced to a nonlinear system in only two unknowns, the transmembrane potential V and the intracellular calcium concentration [Ca]( i ). By numerical approaches appropriate to bifurcation problems, sections in the static bifurcation diagram were determined. For a variable steady depolarizing or hyperpolarizing current (I (st)), the corresponding projection of the static bifurcation diagram in the (I (st), V) plane is complex, featuring three branches of stationary solutions joined by two limit points. On the upper branch oscillations can occur, being either damped at a stable focus or diverted to the lower branch of stable stationary solutions when reaching the unstable manifold of a homoclinic saddle, thus resulting in early after-depolarizations (EADs). The middle branch of solutions is a series of unstable saddle points, while the lower one a series of stable nodes. For variable slow inward and K(+) current maximal conductances (g (si) and g (K)), in a range between 0 and 4-fold normal values, the dynamics is even more complex, and in certain instances sustained oscillations tending to a limit cycle appear. All these types of behavior were correctly predicted by linear stability analysis and bifurcation theory methods, leading to identification of Hopf bifurcation points, limit points of cycles and period doubling bifurcations. In particular settings, e.g. one-fifth-of-normal g (si), EADs and sustained high amplitude oscillations due to an unstable resting state may occur simultaneously.

Incremental parameter evaluation from incomplete data with application to the population pharmacology of anticoagulants.

We develop a method for parameter evaluation from incomplete data. Improved estimates of the desired parameters are evaluated step by step, from experiment to experiment by using both Bayesian and informational methods. We make dynamical, improved predictions while the experiments are still going on and keep and interpret information about local fluctuations, which is lost on applying global techniques. The input of information in small packets leads to semi-analytic methods for data processing. An evolution criterion for parameter evaluation, similar to Fisher's theorem of population selection, is derived. We develop direct processing methods, which can be applied to low dimensional systems, semi-analytic methods based on direct or double logarithmic phase expansions, steepest descent approaches, variation and perturbation methods. The techniques are illustrated by developing a method of long-term planning of treatments with oral anticoagulants based on limited clinical data. The efficiency of treatment by oral anticoagulants depends strongly on various anthropometric and genotypic factors, which lead to large variations of the clinical response. We use the clinical data, which accumulates from medical consultations, for extracting improved, incremental information about the statistical properties of the kinetic and anthropometric parameters for a given patient, which in turn is used for making repeated, improved clinical predictions as the treatment proceeds.

On anti-portfolio effects in science and technology with application to reaction kinetics, chemical synthesis, and molecular biology.

The portfolio effect is the increase of the stability of a system to random fluctuations with the increase of the number of random state variables due to spreading the risk among these variables; many examples exist in various areas of science and technology. We report the existence of an opposite effect, the decrease of stability to random fluctuations due to an increase of the number of random state variables. For successive industrial or biochemical processes of independent, random efficiencies, the stability of the total efficiency decreases with the increase of the number of processes. Depending on the variables considered, the same process may display both a portfolio as well as an anti-portfolio behavior. In disordered kinetics, the activation energy of a reaction or transport process is the result of a sum of random components. Although the total activation energy displays a portfolio effect, the rate coefficient displays an anti-portfolio effect. For random-channel kinetics, the stability of the total rate coefficient increases with the average number of reaction pathways, whereas the stability of the survival function has an opposite behavior: it decreases exponentially with the increase of the average number of reaction pathways (anti-portfolio effect). In molecular biology, the total rate of a nucleotide substitution displays a portfolio effect, whereas the probability that no substitutions occur displays an anti-portfolio effect, resulting in faster evolutionary processes due to fluctuations. The anti-portfolio effect emerges for products of random variables or equations involving multiplicative convolution products.

Susceptibility for ventricular tachycardia and the correlation between depolarization and orthogonal components of repolarization.

OBJECTIVE: There is a continuing need of methods to identify subgroups of patients at high risk of ventricular arrhythmias, in particular after myocardial infarction (MI). METHODS: We performed a singular value decomposition of repolarization potentials in individual recordings in 134 healthy males, in 203 males with old MI and without documented sustained ventricular tachycardia (VT) and in 104 MI males with documented VT. We considered the absolute correlation coefficient between the first orthogonal component, constructed by matrix multiplication of the first left and right singular vectors and the QRS integral (RT1) and a similar index for the second component (RT2). RESULTS: Abnormally high (more than two standard deviations above the mean) value of the RT1 had a 89% specificity for VT in MI patients. Abnormally low RT2 had specificity of 87%. Both indices combined had a 97% specificity. However, sensitivity of the combined indices was only 13%. CONCLUSION: Abnormalities in the correlation of orthogonal components of repolarization with depolarization are highly specific for a small group of patients with old myocardial infarction at high risk of ventricular tachycardia.

Prognostic value of heart rate variability after acute myocardial infarction.

BACKGROUND: Prognosis after acute myocardial infarction (AMI) may be influenced by autonomic dysfunction that can be evaluated by assessment of heart rate variability (HRV). Its predictive value resulted from studies performed prior to large scale use of reperfusion therapy. We assessed the prognostic value of HRV parameters 1 year after AMI in patients treated conventionally or by a reperfusion method in the first 12 hours from onset. MATERIAL/METHODS: We included 463 consecutive patients with AMI (312 M, 151 F) 60.6+/-13.0 years old. 211 were treated by thrombolysis or primary PTCA, the other 251 patients receiving conventional therapy. Time-domain (SDNN, rMSSD) and frequency-domain (LF, HF, total power) HRV parameters were calculated from 24-hour Holter ECG recordings 10-20 days after AMI. The primary endpoint was one-year total mortality and sudden cardiac death. RESULTS: The incidence of cardiac death was 14.7%, while that of sudden death was 4.8%. Both were higher in patients treated conventionally. Patients treated by reperfusion had higher HRV parameters reflecting both vagal and sympathetic activity (SDNN, total spectral power) as well as those expressing only vagal output (rMSSD, HF power) than conventionally treated subjects. The variables independently correlating with 1-year survival were SDNN<50 msec, rMSSD<20 msec, LF/HF>2, non-sustained ventricular tachycardia, and left ventricular ejection fraction <40%. CONCLUSIONS: HRV parameters have prognostic value independent from left ventricular ejection fraction and spontaneous ventricular arrhythmias one year after AMI. Reduction of mortality risk by reperfusion therapy does not decrease the prognostic utility of HRV after AMI.